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CHAPTER 1

INTRODUCTION

1.

Increase in design speed leads to more slender aircrafts with thinner

wings and therefore less stiff structure that leads to a phenomenon known as Aeroelasticity. Aeroelasticity studies the effects of interacting aerodynamic, elastic and inertia forces on aircraft structures. In order to demonstrate the interdisciplinary nature of aeroelasticity Collar created the famous triangle of aeroelasticity, which is shown in Figure 1.1[1]. 2.

In all Aeroelastic problems a common characteristics is observed: the

aerodynamic forces give rise to structural deformations. These structural deformations change the aerodynamic forces and in turn the structural deformations are changed again. This process repeats until a state of equilibrium or, undesirably, a failure is reached.

3.

Aeroelastic problems occur due to the elastic behaviour of aircraft

structures. In other words, if the structures were perfectly rigid then Aeroelastic problems would not have occurred. Increasing the stiffness of an aircraft may be achieved by the use of recent, high technology materials or by increasing the thickness of the structure that results in weight penalty, which are both far from being cost effective solutions. On the other hand, increasing the rigidity of the structure will have unfavourable effects, as it will not necessarily protect the passengers or the payload from sudden gusts.

4.

Most common Aeroelastic effects (problems) that are encountered

include Divergence, Control Reversal, Limit Cycle Oscillation (LCO), Flutter etc. These Aeroelastic problems are highly nonlinear in nature and therefore require high fidelity computational fluid dynamics (CFD) techniques coupled 1 RESTRICTED

RESTRICTED with high fidelity computation structural dynamics (CSD) techniques for their accurate prediction [1]. 5.

Besides predicting Aeroelastic problems, this coupling of CFD and CSD

can be used to compute the aerodynamics of flow around a wing more realistically. Traditionally a rigid wing is immersed in flow in CFD analysis but now with this technique flexibility of wing is also included thus resulting in better correlation between experimental and CFD results [2].

6.

Project Scope.

The goal of this project is to explore ways through

ANSYS® for doing two-way Fluid Structure Interaction (FSI) and then carrying out Aeroelastic analysis to evaluate structural stability of a wing and a plate. The last part of project scope is to validate the results. These objectives are shown pictorially in Fig 1.2

Fig 1.1 Collar‟s Triangle[1]

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Project Report Outline.

The outline of this project is as follows.

Cases that are studied and their description are in Chapter 2. Chapter 3 includes Two-way FSI in ANSYS. Static Aeroelastic analysis and Dynamic Aeroelastic analysis is described in Chapter 4 and Chapter 5 Respectively. Chapter 6 is about FSI in APDL and FLOTRAN and lastly Chapter 7 is Conclusion.

Fig 1.2 Project Scope

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CHAPTER 2

CASES STUDIED

1.

This chapter includes description of cases that are studied for Static

and Dynamic Aeroelastic stability. For Static Aeroelastic stability a flat plate model is used and AGARD 445.6 wing is used for Dynamic Aeroelastic study. These two models are picked because their experimental results are available. The flat plate model is wind-tunnel tested for Divergence in August 1980 by NASA and results are presented in Ref 3.

2.

AGARD

445.6

is

widely

used

benchmark

in

computational

Aeroelasticity. Aeroelastic experiments are highly expensive and can be destructive, thus this test case is one of the few benchmark cases available in open literature

[4]

. Experimental flutter tests are carried out for this wing in

1960 in NASA Dynamics Tunnel at Langley. The complete description of the model, test, wind-tunnel and results are available in Ref 5. The wing is made up of laminated Mahogany. The wing is orthotropic in nature and vertical holes were drilled in the wing to reduce its stiffness.

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CHAPTER 3

FSI CAPABILITIES IN ANSYS WORKBENCH®

1.

This chapter includes the details of how two-way FSI is carried out in

ANYS®. Fluid-Structure Interaction (FSI) analysis is an example of a multiphysics problem where the interaction between two different analyses is taken into account. The FSI analysis involves performing a structural analysis in the Mechanical application taking into account the interaction with the corresponding fluid or previous CFD analysis

2.

There are two ways to carry out FSI in ANSYS®; one is through

MULTIFIELD solver, an automated tool for solving coupled field problems and secondly is through File based load transfer technique. Multifield solver supersedes the file based procedure and provides a robust, accurate and easy to use tool for solving coupled-field problems.

3.

There were two choices were solving the fluid part of analysis, either to

use Fluent or CFX. CFX was chosen because it is written in ANSYS manual that two-way FSI is only possible in ANSYS and CFX solvers [6].

Demonstration FSI Run 4.

The first task was to simulate two-way FSI in ANSYS. This task was

accomplished by carrying out two-way FSI using Multifield solver of a simple plate. Static analysis module is coupled with Fluid analysis as shown in Fig 3.1 so that they can exchange loads and deformation.

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Fig 3.1 Coupling of Fields

Methodology 5.

Modelling.

Plate made up of Structural Steel was modelled in Design

Modeller as shown in Fig 3.2. Design Modeller is the modelling package offered in workbench. Design modeller provides an easy way to model complex geometries and has most of the features that commercial modelling software offer. One can also import model to Design modeller from other modelling software. The best advantage of modelling geometry in Design modeller is that you don‟t need to clean geometry for meshing and further processing.

Fig 3.2 2D Plate and Domain 6 RESTRICTED

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6.

Mesh and Flow Setup.

Fluid and structural parts are meshed

separately in meshing applications. Mesh of structural and fluid part does not need to be conformal for simulating two-way FSI in workbench environment. Domain is made to have standard atmospheric air. All the boundaries are set to wall and plate is given an initial disturbance.

7.

Solver.

provides

Two-way FSI is solved in CFX-Solver. CFX-Solver

options for restarting analysis,

memory allocation, Parallel

processing etc. It automatically adds the CFX-Pre setup file and Structural setup file to be solved. You can also manually specify the location from where it should pick the file to be solved. It manages the all the data transfer across flow and structural physics. You can press the stop button to stop the run but CFX-Solver will stop the sun only when time-step is complete. It also plot different monitors and residuals with each time-step.

8.

Solution.

The plate was given an initial disturbance and under this

disturbance it started vibratory motion. This motion of plate is communicated to Fluid solver which exerts a force in opposite direction due to presence of fluid in the domain and hence this motion of plate is damped in this way. Figure 3.3 shows the displacement of tip of the plate. This damping motion of plate showed that forces and displacements are communicated between the two physics or in other words two-way FSI is simulated.

9.

Post Processing. Post processing is done in CFD post. CFD post

provides various tools to analyze the results; One can make graphs, tables, and plot stream lines, iso-surfaces, etc. CFD post also provides the ability to make videos of time-changing quantities such as deformations, streamlines, pressure contours etc. Fig 3.4 and Fig 3.5 show the stresses in plate at 1st time-step and at 10th time-step, respectively. The decrease in stress level shows that deformation is damped by the flow.

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Fig.3.3 Tip Displacement

Fig 3.4 Stress at 1st time-step

Fig 3.5 Stress at 5TH time-step

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CHAPTER 4

STATIC AEROELASTIC ANALYSIS

1.

After simulating two-way FSI successfully, the next task was to validate

the FSI by finding Aeroelastic structural stability parameters (Divergence and Flutter) and comparing them with analytical or experimental results. First the static Aeroelastic structural stability (Divergence) was considered. A flat wing model is picked for this test as experimental and analytical results are available for this model

[3]

. This model is made up of aluminium alloy.

Divergence velocity is computed for this model, Divergence velocity is defined as the minimum velocity at which the structure continues to deform to the point of failure. The computed Divergence velocity is then compared with the experimental results.

Methodology

2.

Model.

All models were constructed from 2.29mm thick plate with

rounded leading and trailing edges

[3]

. Transition strips with a width of 0.025

times chord were added to both upper and lower sides of all the models

[3]

.

The model and domain are created in geometry module of ANSYS® workbench, Design modeller. Wing geometry is shown in Fig 4.1. The dimensions and material properties of the wing are given in Table 4.1. The flat wing was experimentally tested at forward sweep of 30˚and 15˚.

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Fig 4.1 Geometry of Model

Table 4.1 Dimension and Material Properties of Flat Wing Model

3.

Thickness(mm) Density(Kg/m3)

Young’s Modulus

Model

Span(m)

30˚ Forward Sweep

.508

2.29

7850

2E11

15˚ Forward Sweep

.508

2.29

7850

2E11

Mesh.

Meshing of structural and fluid is done in ANSYS meshing

application which is not very specialized meshing software and does not provide greater control over mesh settings. Moreover in coupled analysis you cannot import mesh from some other software like Gambit, ICEM, etc.

4.

Structural Setup.

The next step after meshing is to setup the

structural model. In this step loads and constraints are applied on structural model. As the model which was experimentally tested, was having a fix root 10 RESTRICTED

RESTRICTED so a fixed root constraint is applied to model. All other faces of structural model are declared as fluid structure interface, the faces across which loads are to be transferred between structural and fluid field. Nonlinear geometry and solution options are also set here. One can also specify the number of iterations after which it would save ANSYS result file; this is required for restarting multi-field analysis. MFRC command is used in ANSYS Mechanical environment to set number of iterations after which ANSYS result file is saved. 5.

Flow Setup.

As the fluid part is solved in CFX so the next step

is to setup flow physics in CFX-Pre. During this step we selects flow properties, apply boundary conditions to flow boundaries, selects type of analysis (transient or steady), Total time of analysis, time-step, turbulence model etc. Flow properties are selected as that of air at 25 ˚C. Transient analysis type was selected for better accuracy. CFX has four boundary condition types namely, inlet, outlet, wall and opening. The boundary conditions assigned include an inlet; outlet and rest of boundaries are assigned as wall. Plate faces are given boundary condition of wall and then further it is specified as faces across which load are to be transferred between physics. The boundary distances from the model are same as used during the wind-tunnel testing of the model. K epsilon turbulence model was selected as it has been proven stable and numerically robust and has well established regime of predictive capability. For general purpose simulations, k-epsilon model offers a good compromise in terms of accuracy and robustness. Multifield analysis requires three types of loops to be setup, Time loop, Coupling/Stagger loop and convergence loop. All these loops are set in CFXPre. Description of each loop is given below and pictorially shown in Fig 4.2 (a)

Time Loop: Amount of time one want the analysis to run. In this loop we specify the time-step and end time.

(b)

Coupling/Stagger Loop: Coupling loop determines the amount of time the data will be shared between structural and fluid solvers per time-step. In this loop we specify the minimum and maximum number of coupling iterations. 11 RESTRICTED

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Convergence/Field Loop: Number of iterations required to solve for flow and structural parameters per coupling step.

Fig 4.2 FSI Loop Setup (courtesy ANSYS)

6.

After setting up the problem the model was tested at several velocities

for divergence. At some velocities the wing deforms to a certain value and then equilibrium is achieved between forces exerted by the flow and the internal forces of the wing but at higher velocities the wing continues to deform under aerodynamic loads until it breaks. The minimum of these velocities at which the wing continues to deform is known as „Divergence Velocity‟. 30˚ Forward Sweep

7.

This flat wing model was tested at 40ms-1, 45ms-1, 48ms-1 and 50ms-

1

.A monitor point is placed at the tip of the flat wing as shown in Fig. 4.3

Displacement of this monitor point is plotted at each time-step. The displacement of this point shows that whether the wing structure is converged or diverged. At certain velocities the wing deforms to a certain position and then reaches equilibrium under the action of aerodynamic forces and internal structural forces but at higher velocities the wing continues to deform under 12 RESTRICTED

RESTRICTED aerodynamic loads. This 30˚ forward sweep wing model deforms to a certain position at 40m/s and then start oscillating not about undeformed position but about a new deformed position. This oscillating motion is damped at each time-step and finally the plate is in some deformed position. Fig 4.4 shows the monitor point displacement at 48 ms-1. The deformed shape of the wing at this velocity is given in Fig 4.5. Monitor Point displacement at 45 m/s is shown in Fig 4.6 As can be seen from the Fig 4.4 and 4.6 that at 48 m/s the flat wing with 30˚ forward sweep diverges where as at 45m/s it is in stable range so considering divergence velocity to be 46.5 m/s where as experimental divergent velocity for this model is 51 m/s.

Fig 4.3 Monitor Point

Fig 4.4 Monitor Point Displacement at 48 m/s

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Fig 4.5 Deformed Shape of Wing at 48m/s

Fig 4.6 Monitor Point Displacement at 45 m/s

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RESTRICTED 15˚ Forward Sweep Model

8.

The flat wing having 15˚ forward sweep was tested at velocity of 80 m/s

the monitor point shows a diverging trend, which is plotted in Fig 4.9 To find Divergence velocity, wing is gain tested at 75 m/s and 78 m/s at which the plate reaches equilibrium so the Divergence speed is between 80m/s and 78 m/s, assuming it to be 79m/s. Fig 4.7 to Fig 4.9 shows displacement of monitor point at velocities on which this model is tested. Experimental divergence velocity obtained for this model is 73 m/s.

Fig 4.7 Monitor Point Displacement at 75 m/s

Fig 4.8 Monitor Point Displacement at 78 m/s 15 RESTRICTED

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Fig 4.9 Monitor Point Displacement at 80 m/s Results

9.

Table 4.2 shows the divergence velocities obtained during this test and

those obtained from wind-tunnel experiment. Fig 4.10 show the divergence dynamics pressures obtained from this test, analytical and experimental.

Table 4.2 Divergence Velocity Comparison Model

Experimental[3]

ANSYS (m/s)

Error

(m/s) 30˚ Forward Sweep

46.5

51

8.8%

15˚ Forward Sweep

79

73

8.2%

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Fig 4.10 Comparison of Divergence Dynamic Pressures

Discussion 10.

Divergence velocity and Divergence dynamic pressure are in good

agreement with experimental results and analytical results. As said in model description that transition strip is not modelled while the actual experimental model was having a transition at both upper surface as well as lower surface. The difference in results can be attributed to this simplification. The other reason for difference in results is that mesh of domain was course so error can be reduced by making the mesh fine but that adds to solution time. From results it can be noted that Divergence speed increases with increase in sweep back.

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CHAPTER 5

DYNAMIC AEROELASTIC ANALYSIS

Introduction

1.

Dynamic Aeroelastic analysis was started after completing the static

Aeroelastic analysis. We need a model for which we can evaluate dynamic Aeroelastic stability and then compare our results with the experimental. As experimentally the dynamic Aeroelastic analysis, i.e. to demonstrate flutter, is highly expensive and can be destructive so we have very few experimental cases available. AGARD 445.6 wing is widely used as benchmark for Aeroelastic analysis as its experimental flutter results are available in open literature

[4]

. This wing is to be checked for dynamic structural stability by

carrying out dynamic Aeroelastic study and then validate the results with experimental results.

2.

Model.

AGARD 445.6 is an experimental wing that has a NACA

65004 airfoil and an aspect ratio of 4, sweep of 45˚ and taper of .6 model is a homogenous and orthotropic in nature

[7]

[7]

. This

. Holes were drilled in the

wing to reduce its stiffness. Fig 5.1 shows the planform of the AGARD 445.6 wing used in the experiment. Material properties of the wing from Ref. 4 are given in table 5.1. The properties are not fully specified in the NASA‟s paper so these properties are picked because using these properties we get the modal frequencies very close to those that were found experimentally.

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Fig 5.1AGARD 445.6 WING Table 5.1 Material Properties of AGARD 445.6 Property Ex Ey Ez Poisson’s Ratio XY Poisson’s Ratio YZ Poisson’s Ratio XZ GXY GYZ GXZ

Value 3.1511E9 4.162E8 4.162E8 .31 .31 .31 4.392E8 4.392E8 4.392E8

Mode Matching

3.

The first step after modelling is modal frequency and mode shape

matching. Complete material properties and model detail are not available in NASA‟s paper, as density of wing, location of holes, complete orthotropic properties are missing. In order to match modal frequencies and mode shapes, density was tuned to 450 kg/m3. Table 5.2 shows the modal frequencies obtained from ANSYS, experimental and from other references. Fig 5.2-Fig 5.5 shows the first four modal shapes. The greatest error in Modal frequency is 5.2% which is acceptable. 19 RESTRICTED

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Table 5.2 Modal Frequencies Comparison Calculated

9.61

40

50.4

96.63

Experimental [8]

9.6

38.10

50.70

98.5

Goura [9]

9.67

36.87

50.26

90

Kolonay [10]

9.63

37.12

50.50

89.94

Percentage Error

.1%

5.2%

.5%

1.8%

Fig 5.2 Mode1

Fig 5.3 Mode 2 20 RESTRICTED

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Fig 5.4 Mode 3

Fig 5.5 Mode 4 Flutter

4.

The general equation of flutter is given as Eq. 5.1

[11]

. Several methods

can be used to solve this equation. These methods can be grouped in two main categories as frequency domain solution methods and Laplace domain (time domain) solution methods. (-ω2 . [M] + i . Ω .[C] + (1+i.g).[K] – q.[Q]).[U] = 0[11] (5.1)

Where, 21 RESTRICTED

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[M] = Generalized mass matrix.

[C] = Generalized damping matrix.

[K] = Generalized stiffness matrix.

[Q] = Generalized aerodynamic forces

Solution Methods

5.

Frequency Domain Methods.

The most commonly used frequency

domain solution methods are K-method and Pk-method. K-method has some disadvantages like the damping value has no physical sense at all velocities except at flutter velocity, so mostly pk-method is used. These methods are available in Patran-Nastran along with a complete Aeroelasticity (flutter) module. Frequency domain methods are most commonly used than time domain methods. The most important reason for this is that aerodynamic theory is more completely developed for simple harmonic motion than arbitrary time dependent motion

[12]

. In frequency domain method we just need

to find the poles of transfer function of the wing. In this method poles are plotted against airspeed and flutter is identified by the lower airspeed at which imaginary part of frequency becomes negative.

6.

Time-Domain Solution.

In Time-domain analysis structure is given

an initial velocity in one of its dominant modes and then time evolution of modal response is noted that whether it grows or decays

[12]

. Time domain

method is the most straight forward way in this computer age but it has the disadvantage that average run time for this simple case is more than 72 hours.

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7.

To perform flutter analysis, the first task was to select model for which

we can perform dynamic aeroelastic analysis and then compare our results of flutter with some experimental or theoretical results available for that model. AGARD 445.6 wing is selected as it is regarded as benchmark in dynamic aeroelastic analysis. Flutter boundary for this wing is calculated at subsonic, supersonic but also at transonic speeds. Methodology is pictorially shown in Fig 5.6. Modal frequencies are matched so the next task was to match flutter boundary at one Mach number. Flutter boundary at a certain Mach number is calculated by keeping the Mach number constant and varying the dynamic pressure as shown in Fig 5.7. Fast Fourier transform (FFT) is then applied to the time history of the motion of tip to find the Flutter frequency. Due to unbearably large solution time I cannot validate the flutter the flutter boundary at all Mach numbers. I tested the wing at Mach=.9 and calculated the flutter boundary at this Mach.

Fig 5.6 Flutter Analysis Methodology

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Fig 5.7 Flutter Workflow Results 8.

The wing is tested for flutter at Mach=.9 and dynamic pressure is varied

and resulting tip motion is noted with each time-step. At each Mach number there is a dynamic pressure at which the tip displacement maintains its amplitude, i.e. it is neither increasing nor decreasing, is called Flutter Boundary for that Mach. The region above flutter boundary is unstable i.e. amplitude of deformation increases; while the region below flutter boundary is stable region i.e. deformation decreases. The stable and unstable region of AGARD 445.6 wing is shown in Fig 5.8. The line labelled Edge Euler is the flutter boundary obtained from Edge software.

Fig 5.8 Stable and Unstable Region of AGARD Wing [16] 24 RESTRICTED

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9. I tested the wing at Mach=.9 and dynamic pressure of 4kPa and 4.52kPa. Fig 5.9 shows the response of wing at 4kPa and Fig 5.10 shows the response of wing at dynamic pressure of 4.52kPa. As can be seen from figures above that wing is in stable range at 4kPa where as it has undergone flutter at 4.520kPa. This means that Flutter boundary is in between 4.520kPa and 4kPa so another test can be done at 4.3kPa but due to limitation of time this run is not completed. The experimental and computed results of flutter boundary are shown in Table 5.3.

Fig 5.9 Tip Displacement at 4kPa

Fig 5.10 Tip Displacement at 4.520kPa

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Mach

Table 5.3 Flutter Boundary Computed Flutter Experimental Flutter Boundary(kPa) Boundary(kPa)

%age Error

.9

4.520

5.11%

4.3kPa

10. Flutter Frequency is obtained by applying FFT on tip displacement graph. Flutter frequency resulted from FFT is as shown in Fig 5.11. Comparison between Computed flutter frequency and experimental flutter frequency is shown in Table 5.4.Difference in frequency can be minimized by making the mesh fine. The initial jump in the frequency graph is due to data corruption that was occurred because power goes off. This data corruption can be seen in tip displacement Fig 5.11.

Fig 5.11 Flutter Frequency

Flutter Frequency

Table 5.4 Flutter Frequency Comparison Computed Experimental 17Hz 20.3Hz

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%age Error 16

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CHAPTER 6

TWO-WAY FSI USING APDL AND FLOTRAN

1.

Introduction. There are two ways to do coupled field analysis (FSI) in

ANSYS, using ANSYS Multi-field solver and Physics file-based procedure. Coupled field analysis using Multi-field solver is explained in Chapter 3. It supersedes the Physics file based procedure and provides a robust, accurate and easy to use tool for solving coupled field problems.

Physics File Based Procedure 2.

“Physics file-based procedure is based on a single finite element mesh

across physics. You create physics files that define the physics environment; these files configure the database and prepare a single mesh for given physics simulation. The general process is to read the first physics file and solve. Then read the next physics file, specify the load to be transferred and solve the second physics file” (ANSYS help//coupled field analysis guide, Chapter 1.1.2.2) 3.

Physics file based procedure is used for simple straight forward

geometries. The difference between physics file based and multi-field solver based coupled field analysis is that in physics file based method we have node to node similar mesh at the interface of fluid and structure where as in multi-field we can have different mesh for structural part and fluid part, so there are special interpolation techniques for load transfer across interface.

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4.

After simulating flutter, it was decided to demonstrate two way FSI in

APDL environment as it offers some advantages over the workbench environment. In workbench we cannot select element type, it automatically selects element type. It assigns SOLID 186 or SOLID 187 for solid (3D) body and hence permitting 3 degree of freedom at each node but in some cases you may want a solid to have six degree of freedom so you want to model it by a shell or beam element but you cannot do it in workbench at least for doing two-way FSI. Secondly two way FSI of only 3D (solid) bodies is allowed in workbench, you cannot two way FSI of 2D geometry. Because of these reason it was decided to demonstrate two-way FSI in APDL as well.

5.

Test Case Description.

The case selected for two-way FSI is 2D

geometry as 3D geometry is already analyzed in workbench. The geometry is modelled in APDL. The object of this test is to show deflection of the beam under aerodynamic loads and resulting change in pressure contours due to deflection of beam. Methodology 6.

After creating geometry in APDL, the flow physics and structural

physics are modelled in APDL environment. First the flow physics is modelled in APDL and the beam is assigned null element type where as the flow is assigned as FLOTRAN 141 that has DOF namely, pressure, velocities and temperature. FLOTRAN boundary conditions are assigned when defining flow physics. Then structural physics is modelled and the flow is assigned as null element type where as beam is assigned as element type Plane 182 that has 2DOF at each node, Ux and Uy. A morphing region is made around the beam, it is the region which is remeshed when structure deforms so that there is node to node matching between flow and structural part. Boundary conditions are applied to structural part (beam) when defining structural physics. Structural and flow boundary conditions are shown in Fig 6.1. 28 RESTRICTED

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Fig 6.1 Boundary Conditions

7.

First the flow physics was solved and the pressure values

corresponding to each node is saved in a file. Then structural physics was solved and the pressures obtained from flow analysis are applied on the nodes of beam. The beam deformation causes the mesh to deform. APDL environment requires node to node matching of mesh for load transfer among physics. The deformation disturbs the node to node matching of flow and structural physics so the morphing area is remeshed to match structural nodes with the flow nodes and then again the flow physics is solved on deformed geometry and the pressure is applied to structure and then again the morphing area is remeshed. This procedure continues until the convergence criteria reaches as in my case it is the motion of beam, if the difference in displacement of beam in two consecutive analyses is less than .05, end the 29 RESTRICTED

RESTRICTED solution. Methodology is shown pictorial in Fig 6.2. Fig 6.3 shows the displacement of tip at with each load step.

Fig 6.2 FSI Methodology in APDL FLOTRAN

Fig 6.3 Tip Displacement Vs Time-step 30 RESTRICTED

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8.

Post processing is also done sequentially, the flow physics is read and

then you can post process flow analysis. Fig 6.4 shows streamlines around the beam. Fig 6.5 shows velocity plot along the path line shown in Fig 6.1. Then structural physics is read and stresses, deformation etc. were found in the beam. Fig 6.6 and Fig 6.7 shows the Von-mises stress for first load step and last load step respectively.

Fig 6.4 Streamlines around Beam

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Fig 6.5 Velocity along the Path line

Fig 6.6 Von-Mises at first step

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Fig 6.7 Von-mises Stress at last step

Results and Discussion 9.

Two-way FSI has been successfully demonstrated in ANSYS APDL

and FLOTRAN. It can be seen that peak stress at first load step is 29% higher than the peak stress of final load step. This shows that considering the effect of displaced geometry on the flow makes significant changes in the stresses of structure.

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CHAPTER 7

CONCLUSIONS AND RECOMMENDATIONS

1.

The objectives of project are successfully achieved. Flutter is never

been performed in ANSYS Workbench but I am able to perform flutter and calculate flutter boundary at one Mach number. Two-way FSI has been demonstrated in both WORKBENCH and APDL. Only 2D FSI has been demonstrated in APDL because in 3D, Mesh morphing is not that easily done as in 2D. WORKBENCH offers an easy way for doing FSI but the control it provides is less e.g., we can select element type for the model, it automatically selects some solid element. WORKBENCH also offers the flexibility to do FSI of large and complicated models. Normal solution time for doing two-way FSI exceeds 24 hours. You can run the solution on multiple machines to reduce solution time.

2.

Commonly used methods for solution of flutter equation are frequency

domain methods as they provide a quick solution but ANSYS works in time domain that‟s why the time for one flutter analysis of simple wing is unbearably large and also one has to apply Fourier Transform to find out the frequency of flutter. The time taken by one flutter analysis is greater than 72 hours. Flutter boundary is found at only one Mach number due to large solution time and the result of flutter boundary is in good agreement with experimental.

3.

Divergence results obtained in this project are in acceptable accuracy.

These results can be made more accurate by avoiding simplifications in the model and making the mesh more refine however both factors increase solution time. 34 RESTRICTED

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RECOMMENDATIONS

4.

Some recommendations after doing this project are listed below,

(a)

Flutter to be demonstrated with some other software that uses frequency methods for solution, so that to check what benefits frequency domain solution offers over time domain solution.

(b)

Calculate flutter boundary of some real aircraft wing using this method as this method is verified.

(c)

Writing a user defined code that will make ANSYS show modal responses with each time-step.

(d)

Fluid Structure Interaction of jet engine turbine blade should be carried out.

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BIBLIOGRAPHY

[1]

Joseph P.Hepp, Static Aeroelastic analysis of ARW-2 wing including

correlation with experiment, Duke University.

[2]

Mehrdad Farhangnia, G. Guruswamy, Sedat Biringen, Transonic-Buffet

Associated Aeroelasticity of a Supercritical Wing. AIAA Paper 96-0286, Jan 1996.

[3]

Rodney h. Ricket, Robert V. Dogget, Wind-Tunnel Experiments on

Divergence of Forward Swept Wings, NASA technical report 1685, Aug 1980

[4]

Saygin Ayabakan, LOOSELY-COUPLED FLUTTER ANALYSIS OF

AGARD WING 445.6H

[5]

E. Carson Yates, Jr., Norman S. Land, Jerome T. Foughner, NASA

technical note D-1616, measured and calculated subsonic and transonic flutter characteristics of a 45 deg swept wing in air and Freon-12

in the

Langley transonic Dynamics tunnel, Jan 1963

[6]

ANSYS help: // Mechanical (formerly Simulation) // The Mechanical

Application Approach // Special Analysis Topics // Fluid-Structure Interaction (FSI)

[7]

NASA Technical memorandum 100492, AGARD Standard Aeroelastic

configuration for dynamic response. Candidate configuration 1, wing 445.6

[8]

AGARD Report No. 765, AGARD Standard Aeroelastic configuration

for dynamic response. Candidate configuration 1, wing 445.6

36 RESTRICTED

RESTRICTED [9]

G. S. L Goura, Time marching analysis of flutter using Computational

Fluid Dynamics, Ph. D. thesis, University of Glasgow, 2001.

[10]

R. M. Kolonay, Unsteady aeroelastic optimization in the transonic

regime, Ph. D. thesis, Purdue University, 1996.

[11]

Umut Susuz, Aeroelastic analysis of unmanned aerial vehicle, Middle

East Technical University.

[12]

Earl H Dowell Kenneth C. Hall, A Modern Course in Aeroelasticity.

[13]

Ryan J. Beaubine, Fred Niztche, Daniel Feszty, Time and Frequency

domain solution for the AGARD 445.6 wing, Carlton University Ontario.

[14]

X.G. Hua, Z.Q.Chen, Full-order and Multi-mode flutter analysis using

ANSYS, Jan 2008.

[15]

Howard J. Conyers, Earl H. Dowell, Kenneth C. Hall, Aeroelastic

studies of a Rectangular wing with a hole: correlation of theory and experiment.

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View more...
CHAPTER 1

INTRODUCTION

1.

Increase in design speed leads to more slender aircrafts with thinner

wings and therefore less stiff structure that leads to a phenomenon known as Aeroelasticity. Aeroelasticity studies the effects of interacting aerodynamic, elastic and inertia forces on aircraft structures. In order to demonstrate the interdisciplinary nature of aeroelasticity Collar created the famous triangle of aeroelasticity, which is shown in Figure 1.1[1]. 2.

In all Aeroelastic problems a common characteristics is observed: the

aerodynamic forces give rise to structural deformations. These structural deformations change the aerodynamic forces and in turn the structural deformations are changed again. This process repeats until a state of equilibrium or, undesirably, a failure is reached.

3.

Aeroelastic problems occur due to the elastic behaviour of aircraft

structures. In other words, if the structures were perfectly rigid then Aeroelastic problems would not have occurred. Increasing the stiffness of an aircraft may be achieved by the use of recent, high technology materials or by increasing the thickness of the structure that results in weight penalty, which are both far from being cost effective solutions. On the other hand, increasing the rigidity of the structure will have unfavourable effects, as it will not necessarily protect the passengers or the payload from sudden gusts.

4.

Most common Aeroelastic effects (problems) that are encountered

include Divergence, Control Reversal, Limit Cycle Oscillation (LCO), Flutter etc. These Aeroelastic problems are highly nonlinear in nature and therefore require high fidelity computational fluid dynamics (CFD) techniques coupled 1 RESTRICTED

RESTRICTED with high fidelity computation structural dynamics (CSD) techniques for their accurate prediction [1]. 5.

Besides predicting Aeroelastic problems, this coupling of CFD and CSD

can be used to compute the aerodynamics of flow around a wing more realistically. Traditionally a rigid wing is immersed in flow in CFD analysis but now with this technique flexibility of wing is also included thus resulting in better correlation between experimental and CFD results [2].

6.

Project Scope.

The goal of this project is to explore ways through

ANSYS® for doing two-way Fluid Structure Interaction (FSI) and then carrying out Aeroelastic analysis to evaluate structural stability of a wing and a plate. The last part of project scope is to validate the results. These objectives are shown pictorially in Fig 1.2

Fig 1.1 Collar‟s Triangle[1]

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Project Report Outline.

The outline of this project is as follows.

Cases that are studied and their description are in Chapter 2. Chapter 3 includes Two-way FSI in ANSYS. Static Aeroelastic analysis and Dynamic Aeroelastic analysis is described in Chapter 4 and Chapter 5 Respectively. Chapter 6 is about FSI in APDL and FLOTRAN and lastly Chapter 7 is Conclusion.

Fig 1.2 Project Scope

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CHAPTER 2

CASES STUDIED

1.

This chapter includes description of cases that are studied for Static

and Dynamic Aeroelastic stability. For Static Aeroelastic stability a flat plate model is used and AGARD 445.6 wing is used for Dynamic Aeroelastic study. These two models are picked because their experimental results are available. The flat plate model is wind-tunnel tested for Divergence in August 1980 by NASA and results are presented in Ref 3.

2.

AGARD

445.6

is

widely

used

benchmark

in

computational

Aeroelasticity. Aeroelastic experiments are highly expensive and can be destructive, thus this test case is one of the few benchmark cases available in open literature

[4]

. Experimental flutter tests are carried out for this wing in

1960 in NASA Dynamics Tunnel at Langley. The complete description of the model, test, wind-tunnel and results are available in Ref 5. The wing is made up of laminated Mahogany. The wing is orthotropic in nature and vertical holes were drilled in the wing to reduce its stiffness.

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CHAPTER 3

FSI CAPABILITIES IN ANSYS WORKBENCH®

1.

This chapter includes the details of how two-way FSI is carried out in

ANYS®. Fluid-Structure Interaction (FSI) analysis is an example of a multiphysics problem where the interaction between two different analyses is taken into account. The FSI analysis involves performing a structural analysis in the Mechanical application taking into account the interaction with the corresponding fluid or previous CFD analysis

2.

There are two ways to carry out FSI in ANSYS®; one is through

MULTIFIELD solver, an automated tool for solving coupled field problems and secondly is through File based load transfer technique. Multifield solver supersedes the file based procedure and provides a robust, accurate and easy to use tool for solving coupled-field problems.

3.

There were two choices were solving the fluid part of analysis, either to

use Fluent or CFX. CFX was chosen because it is written in ANSYS manual that two-way FSI is only possible in ANSYS and CFX solvers [6].

Demonstration FSI Run 4.

The first task was to simulate two-way FSI in ANSYS. This task was

accomplished by carrying out two-way FSI using Multifield solver of a simple plate. Static analysis module is coupled with Fluid analysis as shown in Fig 3.1 so that they can exchange loads and deformation.

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Fig 3.1 Coupling of Fields

Methodology 5.

Modelling.

Plate made up of Structural Steel was modelled in Design

Modeller as shown in Fig 3.2. Design Modeller is the modelling package offered in workbench. Design modeller provides an easy way to model complex geometries and has most of the features that commercial modelling software offer. One can also import model to Design modeller from other modelling software. The best advantage of modelling geometry in Design modeller is that you don‟t need to clean geometry for meshing and further processing.

Fig 3.2 2D Plate and Domain 6 RESTRICTED

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6.

Mesh and Flow Setup.

Fluid and structural parts are meshed

separately in meshing applications. Mesh of structural and fluid part does not need to be conformal for simulating two-way FSI in workbench environment. Domain is made to have standard atmospheric air. All the boundaries are set to wall and plate is given an initial disturbance.

7.

Solver.

provides

Two-way FSI is solved in CFX-Solver. CFX-Solver

options for restarting analysis,

memory allocation, Parallel

processing etc. It automatically adds the CFX-Pre setup file and Structural setup file to be solved. You can also manually specify the location from where it should pick the file to be solved. It manages the all the data transfer across flow and structural physics. You can press the stop button to stop the run but CFX-Solver will stop the sun only when time-step is complete. It also plot different monitors and residuals with each time-step.

8.

Solution.

The plate was given an initial disturbance and under this

disturbance it started vibratory motion. This motion of plate is communicated to Fluid solver which exerts a force in opposite direction due to presence of fluid in the domain and hence this motion of plate is damped in this way. Figure 3.3 shows the displacement of tip of the plate. This damping motion of plate showed that forces and displacements are communicated between the two physics or in other words two-way FSI is simulated.

9.

Post Processing. Post processing is done in CFD post. CFD post

provides various tools to analyze the results; One can make graphs, tables, and plot stream lines, iso-surfaces, etc. CFD post also provides the ability to make videos of time-changing quantities such as deformations, streamlines, pressure contours etc. Fig 3.4 and Fig 3.5 show the stresses in plate at 1st time-step and at 10th time-step, respectively. The decrease in stress level shows that deformation is damped by the flow.

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Fig.3.3 Tip Displacement

Fig 3.4 Stress at 1st time-step

Fig 3.5 Stress at 5TH time-step

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CHAPTER 4

STATIC AEROELASTIC ANALYSIS

1.

After simulating two-way FSI successfully, the next task was to validate

the FSI by finding Aeroelastic structural stability parameters (Divergence and Flutter) and comparing them with analytical or experimental results. First the static Aeroelastic structural stability (Divergence) was considered. A flat wing model is picked for this test as experimental and analytical results are available for this model

[3]

. This model is made up of aluminium alloy.

Divergence velocity is computed for this model, Divergence velocity is defined as the minimum velocity at which the structure continues to deform to the point of failure. The computed Divergence velocity is then compared with the experimental results.

Methodology

2.

Model.

All models were constructed from 2.29mm thick plate with

rounded leading and trailing edges

[3]

. Transition strips with a width of 0.025

times chord were added to both upper and lower sides of all the models

[3]

.

The model and domain are created in geometry module of ANSYS® workbench, Design modeller. Wing geometry is shown in Fig 4.1. The dimensions and material properties of the wing are given in Table 4.1. The flat wing was experimentally tested at forward sweep of 30˚and 15˚.

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Fig 4.1 Geometry of Model

Table 4.1 Dimension and Material Properties of Flat Wing Model

3.

Thickness(mm) Density(Kg/m3)

Young’s Modulus

Model

Span(m)

30˚ Forward Sweep

.508

2.29

7850

2E11

15˚ Forward Sweep

.508

2.29

7850

2E11

Mesh.

Meshing of structural and fluid is done in ANSYS meshing

application which is not very specialized meshing software and does not provide greater control over mesh settings. Moreover in coupled analysis you cannot import mesh from some other software like Gambit, ICEM, etc.

4.

Structural Setup.

The next step after meshing is to setup the

structural model. In this step loads and constraints are applied on structural model. As the model which was experimentally tested, was having a fix root 10 RESTRICTED

RESTRICTED so a fixed root constraint is applied to model. All other faces of structural model are declared as fluid structure interface, the faces across which loads are to be transferred between structural and fluid field. Nonlinear geometry and solution options are also set here. One can also specify the number of iterations after which it would save ANSYS result file; this is required for restarting multi-field analysis. MFRC command is used in ANSYS Mechanical environment to set number of iterations after which ANSYS result file is saved. 5.

Flow Setup.

As the fluid part is solved in CFX so the next step

is to setup flow physics in CFX-Pre. During this step we selects flow properties, apply boundary conditions to flow boundaries, selects type of analysis (transient or steady), Total time of analysis, time-step, turbulence model etc. Flow properties are selected as that of air at 25 ˚C. Transient analysis type was selected for better accuracy. CFX has four boundary condition types namely, inlet, outlet, wall and opening. The boundary conditions assigned include an inlet; outlet and rest of boundaries are assigned as wall. Plate faces are given boundary condition of wall and then further it is specified as faces across which load are to be transferred between physics. The boundary distances from the model are same as used during the wind-tunnel testing of the model. K epsilon turbulence model was selected as it has been proven stable and numerically robust and has well established regime of predictive capability. For general purpose simulations, k-epsilon model offers a good compromise in terms of accuracy and robustness. Multifield analysis requires three types of loops to be setup, Time loop, Coupling/Stagger loop and convergence loop. All these loops are set in CFXPre. Description of each loop is given below and pictorially shown in Fig 4.2 (a)

Time Loop: Amount of time one want the analysis to run. In this loop we specify the time-step and end time.

(b)

Coupling/Stagger Loop: Coupling loop determines the amount of time the data will be shared between structural and fluid solvers per time-step. In this loop we specify the minimum and maximum number of coupling iterations. 11 RESTRICTED

RESTRICTED (c)

Convergence/Field Loop: Number of iterations required to solve for flow and structural parameters per coupling step.

Fig 4.2 FSI Loop Setup (courtesy ANSYS)

6.

After setting up the problem the model was tested at several velocities

for divergence. At some velocities the wing deforms to a certain value and then equilibrium is achieved between forces exerted by the flow and the internal forces of the wing but at higher velocities the wing continues to deform under aerodynamic loads until it breaks. The minimum of these velocities at which the wing continues to deform is known as „Divergence Velocity‟. 30˚ Forward Sweep

7.

This flat wing model was tested at 40ms-1, 45ms-1, 48ms-1 and 50ms-

1

.A monitor point is placed at the tip of the flat wing as shown in Fig. 4.3

Displacement of this monitor point is plotted at each time-step. The displacement of this point shows that whether the wing structure is converged or diverged. At certain velocities the wing deforms to a certain position and then reaches equilibrium under the action of aerodynamic forces and internal structural forces but at higher velocities the wing continues to deform under 12 RESTRICTED

RESTRICTED aerodynamic loads. This 30˚ forward sweep wing model deforms to a certain position at 40m/s and then start oscillating not about undeformed position but about a new deformed position. This oscillating motion is damped at each time-step and finally the plate is in some deformed position. Fig 4.4 shows the monitor point displacement at 48 ms-1. The deformed shape of the wing at this velocity is given in Fig 4.5. Monitor Point displacement at 45 m/s is shown in Fig 4.6 As can be seen from the Fig 4.4 and 4.6 that at 48 m/s the flat wing with 30˚ forward sweep diverges where as at 45m/s it is in stable range so considering divergence velocity to be 46.5 m/s where as experimental divergent velocity for this model is 51 m/s.

Fig 4.3 Monitor Point

Fig 4.4 Monitor Point Displacement at 48 m/s

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Fig 4.5 Deformed Shape of Wing at 48m/s

Fig 4.6 Monitor Point Displacement at 45 m/s

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RESTRICTED 15˚ Forward Sweep Model

8.

The flat wing having 15˚ forward sweep was tested at velocity of 80 m/s

the monitor point shows a diverging trend, which is plotted in Fig 4.9 To find Divergence velocity, wing is gain tested at 75 m/s and 78 m/s at which the plate reaches equilibrium so the Divergence speed is between 80m/s and 78 m/s, assuming it to be 79m/s. Fig 4.7 to Fig 4.9 shows displacement of monitor point at velocities on which this model is tested. Experimental divergence velocity obtained for this model is 73 m/s.

Fig 4.7 Monitor Point Displacement at 75 m/s

Fig 4.8 Monitor Point Displacement at 78 m/s 15 RESTRICTED

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Fig 4.9 Monitor Point Displacement at 80 m/s Results

9.

Table 4.2 shows the divergence velocities obtained during this test and

those obtained from wind-tunnel experiment. Fig 4.10 show the divergence dynamics pressures obtained from this test, analytical and experimental.

Table 4.2 Divergence Velocity Comparison Model

Experimental[3]

ANSYS (m/s)

Error

(m/s) 30˚ Forward Sweep

46.5

51

8.8%

15˚ Forward Sweep

79

73

8.2%

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Fig 4.10 Comparison of Divergence Dynamic Pressures

Discussion 10.

Divergence velocity and Divergence dynamic pressure are in good

agreement with experimental results and analytical results. As said in model description that transition strip is not modelled while the actual experimental model was having a transition at both upper surface as well as lower surface. The difference in results can be attributed to this simplification. The other reason for difference in results is that mesh of domain was course so error can be reduced by making the mesh fine but that adds to solution time. From results it can be noted that Divergence speed increases with increase in sweep back.

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CHAPTER 5

DYNAMIC AEROELASTIC ANALYSIS

Introduction

1.

Dynamic Aeroelastic analysis was started after completing the static

Aeroelastic analysis. We need a model for which we can evaluate dynamic Aeroelastic stability and then compare our results with the experimental. As experimentally the dynamic Aeroelastic analysis, i.e. to demonstrate flutter, is highly expensive and can be destructive so we have very few experimental cases available. AGARD 445.6 wing is widely used as benchmark for Aeroelastic analysis as its experimental flutter results are available in open literature

[4]

. This wing is to be checked for dynamic structural stability by

carrying out dynamic Aeroelastic study and then validate the results with experimental results.

2.

Model.

AGARD 445.6 is an experimental wing that has a NACA

65004 airfoil and an aspect ratio of 4, sweep of 45˚ and taper of .6 model is a homogenous and orthotropic in nature

[7]

[7]

. This

. Holes were drilled in the

wing to reduce its stiffness. Fig 5.1 shows the planform of the AGARD 445.6 wing used in the experiment. Material properties of the wing from Ref. 4 are given in table 5.1. The properties are not fully specified in the NASA‟s paper so these properties are picked because using these properties we get the modal frequencies very close to those that were found experimentally.

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Fig 5.1AGARD 445.6 WING Table 5.1 Material Properties of AGARD 445.6 Property Ex Ey Ez Poisson’s Ratio XY Poisson’s Ratio YZ Poisson’s Ratio XZ GXY GYZ GXZ

Value 3.1511E9 4.162E8 4.162E8 .31 .31 .31 4.392E8 4.392E8 4.392E8

Mode Matching

3.

The first step after modelling is modal frequency and mode shape

matching. Complete material properties and model detail are not available in NASA‟s paper, as density of wing, location of holes, complete orthotropic properties are missing. In order to match modal frequencies and mode shapes, density was tuned to 450 kg/m3. Table 5.2 shows the modal frequencies obtained from ANSYS, experimental and from other references. Fig 5.2-Fig 5.5 shows the first four modal shapes. The greatest error in Modal frequency is 5.2% which is acceptable. 19 RESTRICTED

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Table 5.2 Modal Frequencies Comparison Calculated

9.61

40

50.4

96.63

Experimental [8]

9.6

38.10

50.70

98.5

Goura [9]

9.67

36.87

50.26

90

Kolonay [10]

9.63

37.12

50.50

89.94

Percentage Error

.1%

5.2%

.5%

1.8%

Fig 5.2 Mode1

Fig 5.3 Mode 2 20 RESTRICTED

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Fig 5.4 Mode 3

Fig 5.5 Mode 4 Flutter

4.

The general equation of flutter is given as Eq. 5.1

[11]

. Several methods

can be used to solve this equation. These methods can be grouped in two main categories as frequency domain solution methods and Laplace domain (time domain) solution methods. (-ω2 . [M] + i . Ω .[C] + (1+i.g).[K] – q.[Q]).[U] = 0[11] (5.1)

Where, 21 RESTRICTED

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[M] = Generalized mass matrix.

[C] = Generalized damping matrix.

[K] = Generalized stiffness matrix.

[Q] = Generalized aerodynamic forces

Solution Methods

5.

Frequency Domain Methods.

The most commonly used frequency

domain solution methods are K-method and Pk-method. K-method has some disadvantages like the damping value has no physical sense at all velocities except at flutter velocity, so mostly pk-method is used. These methods are available in Patran-Nastran along with a complete Aeroelasticity (flutter) module. Frequency domain methods are most commonly used than time domain methods. The most important reason for this is that aerodynamic theory is more completely developed for simple harmonic motion than arbitrary time dependent motion

[12]

. In frequency domain method we just need

to find the poles of transfer function of the wing. In this method poles are plotted against airspeed and flutter is identified by the lower airspeed at which imaginary part of frequency becomes negative.

6.

Time-Domain Solution.

In Time-domain analysis structure is given

an initial velocity in one of its dominant modes and then time evolution of modal response is noted that whether it grows or decays

[12]

. Time domain

method is the most straight forward way in this computer age but it has the disadvantage that average run time for this simple case is more than 72 hours.

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RESTRICTED Methodology

7.

To perform flutter analysis, the first task was to select model for which

we can perform dynamic aeroelastic analysis and then compare our results of flutter with some experimental or theoretical results available for that model. AGARD 445.6 wing is selected as it is regarded as benchmark in dynamic aeroelastic analysis. Flutter boundary for this wing is calculated at subsonic, supersonic but also at transonic speeds. Methodology is pictorially shown in Fig 5.6. Modal frequencies are matched so the next task was to match flutter boundary at one Mach number. Flutter boundary at a certain Mach number is calculated by keeping the Mach number constant and varying the dynamic pressure as shown in Fig 5.7. Fast Fourier transform (FFT) is then applied to the time history of the motion of tip to find the Flutter frequency. Due to unbearably large solution time I cannot validate the flutter the flutter boundary at all Mach numbers. I tested the wing at Mach=.9 and calculated the flutter boundary at this Mach.

Fig 5.6 Flutter Analysis Methodology

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Fig 5.7 Flutter Workflow Results 8.

The wing is tested for flutter at Mach=.9 and dynamic pressure is varied

and resulting tip motion is noted with each time-step. At each Mach number there is a dynamic pressure at which the tip displacement maintains its amplitude, i.e. it is neither increasing nor decreasing, is called Flutter Boundary for that Mach. The region above flutter boundary is unstable i.e. amplitude of deformation increases; while the region below flutter boundary is stable region i.e. deformation decreases. The stable and unstable region of AGARD 445.6 wing is shown in Fig 5.8. The line labelled Edge Euler is the flutter boundary obtained from Edge software.

Fig 5.8 Stable and Unstable Region of AGARD Wing [16] 24 RESTRICTED

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9. I tested the wing at Mach=.9 and dynamic pressure of 4kPa and 4.52kPa. Fig 5.9 shows the response of wing at 4kPa and Fig 5.10 shows the response of wing at dynamic pressure of 4.52kPa. As can be seen from figures above that wing is in stable range at 4kPa where as it has undergone flutter at 4.520kPa. This means that Flutter boundary is in between 4.520kPa and 4kPa so another test can be done at 4.3kPa but due to limitation of time this run is not completed. The experimental and computed results of flutter boundary are shown in Table 5.3.

Fig 5.9 Tip Displacement at 4kPa

Fig 5.10 Tip Displacement at 4.520kPa

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Mach

Table 5.3 Flutter Boundary Computed Flutter Experimental Flutter Boundary(kPa) Boundary(kPa)

%age Error

.9

4.520

5.11%

4.3kPa

10. Flutter Frequency is obtained by applying FFT on tip displacement graph. Flutter frequency resulted from FFT is as shown in Fig 5.11. Comparison between Computed flutter frequency and experimental flutter frequency is shown in Table 5.4.Difference in frequency can be minimized by making the mesh fine. The initial jump in the frequency graph is due to data corruption that was occurred because power goes off. This data corruption can be seen in tip displacement Fig 5.11.

Fig 5.11 Flutter Frequency

Flutter Frequency

Table 5.4 Flutter Frequency Comparison Computed Experimental 17Hz 20.3Hz

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%age Error 16

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CHAPTER 6

TWO-WAY FSI USING APDL AND FLOTRAN

1.

Introduction. There are two ways to do coupled field analysis (FSI) in

ANSYS, using ANSYS Multi-field solver and Physics file-based procedure. Coupled field analysis using Multi-field solver is explained in Chapter 3. It supersedes the Physics file based procedure and provides a robust, accurate and easy to use tool for solving coupled field problems.

Physics File Based Procedure 2.

“Physics file-based procedure is based on a single finite element mesh

across physics. You create physics files that define the physics environment; these files configure the database and prepare a single mesh for given physics simulation. The general process is to read the first physics file and solve. Then read the next physics file, specify the load to be transferred and solve the second physics file” (ANSYS help//coupled field analysis guide, Chapter 1.1.2.2) 3.

Physics file based procedure is used for simple straight forward

geometries. The difference between physics file based and multi-field solver based coupled field analysis is that in physics file based method we have node to node similar mesh at the interface of fluid and structure where as in multi-field we can have different mesh for structural part and fluid part, so there are special interpolation techniques for load transfer across interface.

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RESTRICTED Two-Way FSI in APDL

4.

After simulating flutter, it was decided to demonstrate two way FSI in

APDL environment as it offers some advantages over the workbench environment. In workbench we cannot select element type, it automatically selects element type. It assigns SOLID 186 or SOLID 187 for solid (3D) body and hence permitting 3 degree of freedom at each node but in some cases you may want a solid to have six degree of freedom so you want to model it by a shell or beam element but you cannot do it in workbench at least for doing two-way FSI. Secondly two way FSI of only 3D (solid) bodies is allowed in workbench, you cannot two way FSI of 2D geometry. Because of these reason it was decided to demonstrate two-way FSI in APDL as well.

5.

Test Case Description.

The case selected for two-way FSI is 2D

geometry as 3D geometry is already analyzed in workbench. The geometry is modelled in APDL. The object of this test is to show deflection of the beam under aerodynamic loads and resulting change in pressure contours due to deflection of beam. Methodology 6.

After creating geometry in APDL, the flow physics and structural

physics are modelled in APDL environment. First the flow physics is modelled in APDL and the beam is assigned null element type where as the flow is assigned as FLOTRAN 141 that has DOF namely, pressure, velocities and temperature. FLOTRAN boundary conditions are assigned when defining flow physics. Then structural physics is modelled and the flow is assigned as null element type where as beam is assigned as element type Plane 182 that has 2DOF at each node, Ux and Uy. A morphing region is made around the beam, it is the region which is remeshed when structure deforms so that there is node to node matching between flow and structural part. Boundary conditions are applied to structural part (beam) when defining structural physics. Structural and flow boundary conditions are shown in Fig 6.1. 28 RESTRICTED

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Fig 6.1 Boundary Conditions

7.

First the flow physics was solved and the pressure values

corresponding to each node is saved in a file. Then structural physics was solved and the pressures obtained from flow analysis are applied on the nodes of beam. The beam deformation causes the mesh to deform. APDL environment requires node to node matching of mesh for load transfer among physics. The deformation disturbs the node to node matching of flow and structural physics so the morphing area is remeshed to match structural nodes with the flow nodes and then again the flow physics is solved on deformed geometry and the pressure is applied to structure and then again the morphing area is remeshed. This procedure continues until the convergence criteria reaches as in my case it is the motion of beam, if the difference in displacement of beam in two consecutive analyses is less than .05, end the 29 RESTRICTED

RESTRICTED solution. Methodology is shown pictorial in Fig 6.2. Fig 6.3 shows the displacement of tip at with each load step.

Fig 6.2 FSI Methodology in APDL FLOTRAN

Fig 6.3 Tip Displacement Vs Time-step 30 RESTRICTED

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8.

Post processing is also done sequentially, the flow physics is read and

then you can post process flow analysis. Fig 6.4 shows streamlines around the beam. Fig 6.5 shows velocity plot along the path line shown in Fig 6.1. Then structural physics is read and stresses, deformation etc. were found in the beam. Fig 6.6 and Fig 6.7 shows the Von-mises stress for first load step and last load step respectively.

Fig 6.4 Streamlines around Beam

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Fig 6.5 Velocity along the Path line

Fig 6.6 Von-Mises at first step

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Fig 6.7 Von-mises Stress at last step

Results and Discussion 9.

Two-way FSI has been successfully demonstrated in ANSYS APDL

and FLOTRAN. It can be seen that peak stress at first load step is 29% higher than the peak stress of final load step. This shows that considering the effect of displaced geometry on the flow makes significant changes in the stresses of structure.

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CHAPTER 7

CONCLUSIONS AND RECOMMENDATIONS

1.

The objectives of project are successfully achieved. Flutter is never

been performed in ANSYS Workbench but I am able to perform flutter and calculate flutter boundary at one Mach number. Two-way FSI has been demonstrated in both WORKBENCH and APDL. Only 2D FSI has been demonstrated in APDL because in 3D, Mesh morphing is not that easily done as in 2D. WORKBENCH offers an easy way for doing FSI but the control it provides is less e.g., we can select element type for the model, it automatically selects some solid element. WORKBENCH also offers the flexibility to do FSI of large and complicated models. Normal solution time for doing two-way FSI exceeds 24 hours. You can run the solution on multiple machines to reduce solution time.

2.

Commonly used methods for solution of flutter equation are frequency

domain methods as they provide a quick solution but ANSYS works in time domain that‟s why the time for one flutter analysis of simple wing is unbearably large and also one has to apply Fourier Transform to find out the frequency of flutter. The time taken by one flutter analysis is greater than 72 hours. Flutter boundary is found at only one Mach number due to large solution time and the result of flutter boundary is in good agreement with experimental.

3.

Divergence results obtained in this project are in acceptable accuracy.

These results can be made more accurate by avoiding simplifications in the model and making the mesh more refine however both factors increase solution time. 34 RESTRICTED

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RECOMMENDATIONS

4.

Some recommendations after doing this project are listed below,

(a)

Flutter to be demonstrated with some other software that uses frequency methods for solution, so that to check what benefits frequency domain solution offers over time domain solution.

(b)

Calculate flutter boundary of some real aircraft wing using this method as this method is verified.

(c)

Writing a user defined code that will make ANSYS show modal responses with each time-step.

(d)

Fluid Structure Interaction of jet engine turbine blade should be carried out.

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BIBLIOGRAPHY

[1]

Joseph P.Hepp, Static Aeroelastic analysis of ARW-2 wing including

correlation with experiment, Duke University.

[2]

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